Simplify the following expression: $\sqrt{75}+\sqrt{48}-\sqrt{12}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{75}+\sqrt{48}-\sqrt{12}$ $= \sqrt{25 \cdot 3}+\sqrt{16 \cdot 3}-\sqrt{4 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{3}+\sqrt{16} \cdot \sqrt{3}-\sqrt{4} \cdot \sqrt{3}$ $= 5\sqrt{3}+4\sqrt{3}-2\sqrt{3}$ Finally, simplify by combining the terms. $= ( 5 + 4 - 2 )\sqrt{3} = 7\sqrt{3}$